Problem: Tiffany is 12 years older than Stephanie. Nineteen years ago, Tiffany was 3 times older than Stephanie. How old is Tiffany now?
Explanation: We can use the given information to write down two equations that describe the ages of Tiffany and Stephanie. Let Tiffany's current age be $t$ and Stephanie's current age be $s$ The information in the first sentence can be expressed in the following equation: $t = s + 12$ Nineteen years ago, Tiffany was $t - 19$ years old, and Stephanie was $s - 19$ years old. The information in the second sentence can be expressed in the following equation: $t - 19 = 3(s - 19)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $t$ , it might be easiest to solve our first equation for $s$ and substitute it into our second equation. Solving our first equation for $s$ , we get: $s = t - 12$ . Substituting this into our second equation, we get the equation: $t - 19 = 3($ $(t - 12)$ $ -$ $ 19)$ which combines the information about $t$ from both of our original equations. Simplifying the right side of this equation, we get: $t - 19 = 3t - 93$ Solving for $t$ , we get: $2 t = 74$ $t = 37$.